1- This key has to be the user password login? Or they are independent keys/passwords?
They are independent passwords. The default "Login" keyring is encrypted upon creation using the user's password, so by default the two passwords match, but you may change either without affecting the other.
When the user is logged in by the desktop manager, an attempt to unlock the keyring using the password used to log the user in is made; if this fails (if the user's password doesn't match the keyring's password), the user is prompted for the keyring's password.
Note that this is the reason why you're being prompted for the keyring's password since you enabled auto-login: auto-login completely bypasses the traditional user / password authentication method, and since there's no password involved at all, there's also no password that could be used to attempt to unlock the keyring.
2- If that dialog opens to get the key (which is "text"), where does this key go? I mean, wouldn't it possible to write a bash script to send this key before the Session Keylocker dialog pops up?
It "goes" to the keyring daemon; I believe Xubuntu by default uses gnome-keyring-daemon.
It's certainly possible to unlock the keyring using the command line / a script, however since in oder to automate the process the keyring's password would have to be stored in plain text somewhere, one might as well argue that if security is not a concern you could just go all the way in and just leave the keyring unencrypted (which obviously has security implications, and admittedly is probably worse than storing the keyring's password in plain text; if someone got a shell running as your user and you left your keyring unencrypted they could just cat it, while if you set up a script to auto-unlock the keyring on graphical login using a password stored in ~/my_cats_name.txt the attacker would have to at least figure out that there's a system in place to auto-unlock the keyring, or, what the password in ~/my_cats_name.txt is good for).